Problem: Solve for $x$ and $y$ using elimination. ${-5x-2y = -35}$ ${3x+2y = 29}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2y$ and $2y$ cancel out. $-2x = -6$ $\dfrac{-2x}{{-2}} = \dfrac{-6}{{-2}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {-5x-2y = -35}\thinspace$ to find $y$ ${-5}{(3)}{ - 2y = -35}$ $-15-2y = -35$ $-15{+15} - 2y = -35{+15}$ $-2y = -20$ $\dfrac{-2y}{{-2}} = \dfrac{-20}{{-2}}$ ${y = 10}$ You can also plug ${x = 3}$ into $\thinspace {3x+2y = 29}\thinspace$ and get the same answer for $y$ : ${3}{(3)}{ + 2y = 29}$ ${y = 10}$